ESTIMATION OF SPATIALLY-VARIABLE AQUIFER HYDRAULIC-PROPERTIES USING KALMAN FILTERING

Spatial variability of aquifer properties and hydraulic heads are mode led as random fields, and their estimates are achieved by Kalman filte ring. The state-space equation is developed from a quasi-analytical so lution of a first-order approximation of the governing stochastic flow equation, In the state-space system, the effects of aquifer heterogen eity and uncertainty in recharge are lumped linearly into a random noi se vector that is correlated in time. To account for the correlated sy stem noise, we reformulate the problem in terms of an augmented-state- space system and use the resulting Kalman filtering recursions to esti mate transmissivities, storativities, and hydraulic heads, simultaneou sly. The filter is applied to a numerical experiment in which the stat istical parameters of log aquifer properties are assumed to be known. The results indicate that under mild head gradients, head measurements alone are of limited value if the objective is to estimate the spatia l distribution of aquifer transmissivity and storativity. Ultimately, measurements of the aquifer properties may be required for reliable es timation of their unknown values.